“…Therefore, f (j,k) + R depends on an integer that can take four values, n + R = 0, 1, 2, 3, and for each of these cases there is a solution where j and k are integers (a case labeled by l + = 0), and a different solution (l + = 1) where they are half-integers. Given one of these solutions for f (j,k) + R , the first equation in (3.24) determines f (j,k) + L and gives a solution of the same form except for a shift by one in n + R and an overall phase factor: 25) where f (j,k) n is given by Eq. (2.37).…”